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Analysis of a Semi-Open Queuing Network with a State Dependent Marked Markovian Arrival Process, Customers Retrials and Impatience

Author

Listed:
  • Chesoong Kim

    (Department of Industrial Engineering, Sangji University, Wonju, Kangwon 26339, Korea)

  • Sergey Dudin

    (Department of Applied Mathematics and Computer Science, Belarusian State University, 4, Nezavisimosti Ave., 220030 Minsk, Belarus
    Department of Applied Informatics and Probability Theory, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, 117198 Moscow, Russia)

  • Alexander Dudin

    (Department of Applied Mathematics and Computer Science, Belarusian State University, 4, Nezavisimosti Ave., 220030 Minsk, Belarus
    Department of Applied Informatics and Probability Theory, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, 117198 Moscow, Russia)

  • Konstantin Samouylov

    (Department of Applied Informatics and Probability Theory, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, 117198 Moscow, Russia)

Abstract

We consider a queuing network with single-server nodes and heterogeneous customers. The number of customers, which can obtain service simultaneously, is restricted. Customers that cannot be admitted to the network upon arrival make repeated attempts to obtain service. The service time at the nodes is exponentially distributed. After service completion at a node, the serviced customer can transit to another node or leave the network forever. The main features of the model are the mutual dependence of processes of customer arrivals and retrials and the impatience and non-persistence of customers. Dynamics of the network are described by a multidimensional Markov chain with infinite state space, state inhomogeneous behavior and special structure of the infinitesimal generator. The explicit form of the generator is derived. An effective algorithm for computing the stationary distribution of this chain is recommended. The expressions for computation of the key performance measures of the network are given. Numerical results illustrating the importance of the account of the mentioned features of the model are presented. The model can be useful for capacity planning, performance evaluation and optimization of various wireless telecommunication networks, transportation and manufacturing systems.

Suggested Citation

  • Chesoong Kim & Sergey Dudin & Alexander Dudin & Konstantin Samouylov, 2019. "Analysis of a Semi-Open Queuing Network with a State Dependent Marked Markovian Arrival Process, Customers Retrials and Impatience," Mathematics, MDPI, vol. 7(8), pages 1-19, August.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:8:p:715-:d:255577
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    References listed on IDEAS

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    1. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 4.
    2. Palmer, Geraint I. & Harper, Paul R. & Knight, Vincent A., 2018. "Modelling deadlock in open restricted queueing networks," European Journal of Operational Research, Elsevier, vol. 266(2), pages 609-621.
    3. Jing Jia & Sunderesh S. Heragu, 2009. "Solving Semi-Open Queuing Networks," Operations Research, INFORMS, vol. 57(2), pages 391-401, April.
    4. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 3.
    5. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 2.
    6. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 2.
    7. Debjit Roy, 2016. "Semi-open queuing networks: a review of stochastic models, solution methods and new research areas," International Journal of Production Research, Taylor & Francis Journals, vol. 54(6), pages 1735-1752, March.
    8. Dhingra, Vibhuti & Kumawat, Govind Lal & Roy, Debjit & Koster, René de, 2018. "Solving semi-open queuing networks with time-varying arrivals: An application in container terminal landside operations," European Journal of Operational Research, Elsevier, vol. 267(3), pages 855-876.
    9. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 4.
    10. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 3.
    11. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 1.
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    Cited by:

    1. Sergey Dudin & Alexander Dudin & Rosanna Manzo & Luigi Rarità, 2024. "Analysis of Semi-open Queueing Network with Correlated Arrival Process and Multi-server Nodes," SN Operations Research Forum, Springer, vol. 5(4), pages 1-29, December.
    2. Igor Bychkov & Alexander Kazakov & Anna Lempert & Maxim Zharkov, 2025. "Modeling and Numerical Analysis of the Severobaikalsk Section of the Baikal–Amur Mainline Considering Environmental Points," Sustainability, MDPI, vol. 17(2), pages 1-23, January.

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